THINK A number written in scientific notation has THREE parts:

Part 1: A number greater than or equal to 1 and less than 10 Part 2: A multiplication symbol – usually x. Part 3: The number 10 with a positive or negative

EXPONENT. Dividing using scientific notation

KNOW IT!

1. Group and decimals and MULTIPLY! 2. ADD the exponents when its MULTIPLICATION 3. SUBTRACT the exponents when it’s DIVISION.

8th Grade Only …NO CALCULATORS ON THIS PORTION… 1. Whichexpressionresultsinarationalnumber?

A)

€

1.5+ 1.5

B)

€

12− 12

C)

€

34

• 34

D)

€

25÷ 25

2. Simplify. (4x)2–4x3

A)

€

x-1

B)

€

12x-1

C)

€

16x2 −4x3

D)

€

16x2 −64x33. Simplify.

€

1.2×10−6

4.8×104

A)

€

2.5×10−2

B)

€

2.5×10−9

C)

€

2.5×10−10

D)

€

2.5×10−11

THINK Rational Numbers can be graphed on a number line. They either terminate (end) or repeat and CAN be written as fractions.

Examples: 4, -2, 3.5, 0.3333,

€

5

6,

€

9 , …

Irrational Numbers are “mixed up decimals” when simplified with no pattern. They never end and never repeat and CAN’T be written as fractions.

Examples:

€

14 = 3.74165… no pattern…

THINK

The exponent is like a … he will “lasso” ONLY what he is “touching.” REMEMBER: When in doubt, EXPAND IT OUT!

Example: (3a)2 – 5a3 = (3a)(3a) – 5a3 = 9a2 – 5a3 Are they like terms? = __________

LIKE TERMS have the SAME BASE and the SAME POWER. Example: 2a2 + 3a2 = 5a2

THINK • In a function, there is ONE unique OUTPUT (y) value for

every INPUT (x) value. • You do not have a function if the same input value results in

2 or more different output values. • You do not have a function if the same “x” value results in 2

or more different y values.

Does each table represent a function? Why or Why Not?

Example 1: YES Example 2: YES Example 3: NO Each INPUT Each INPUT The 2 has MORE than has ONLY 1 has ONLY 1 ONE OUTPUT. OUTPUT. OUTPUT.

THINK “As a function of… guests (g)…” means ___________________ The dependent variable CAN’T be changed – not free. The independent variable CAN change – it is free. In this problem, the dependent variable is c. This means c CAN’T change and is NOT included in the function. What CAN change? Guests (g) *You are looking for the function of guests (g) that shows the number of guests as your independent variable (what will CHANGE). For example:

Guests (g) Equation Cakes (c) 12 1 24 2 36 ?

Which equation/function matches?

4. WhichtableofvaluesdoesNOTrepresentafunction?

5. Thenumberofcakesneededforaparty,c,isdependentuponthe

numberofguestsattheparty,g.Whichequationshowsthenumberofcakesasafunctionofthenumberofguests?

THINK Strategy: Use a ruler to EXTEND the line. Use the line to GUESS and TEST each statement. ONLY 1 is TRUE.

6. Agraphisshown.Whichsituationisrepresentedbythegraph?

7. Annsellsbraceletsfor$4eachandnecklacesfor$8each.Which

inequalityshowsx,thenumberofbracelets,andy,thenumberofnecklacesAnnmustselltomakeatleast$100?

THINK

Math Talk… “each” means x or ÷ “at least” means more than or equal to $100 Where are numbers that are “at least” 100?

Word Equation: Bracelets = x Bracelets and Necklaces = 100 Necklaces = y __x + __y ___ 100

98 99 100 101 102

THINK An Arithmetic Sequence has a COMMON DIFFERENCE. This means you can ADD or SUBTRACT the SAME number from one term to the next.

THINK • PARALLEL lines have EQUAL slopes. • PERPENDICULAR lines have OPPOSITE RECIPROCAL

slopes.

8. Arectangleisdrawnonacoordinategrid.Theequationfor1sideoftherectangleis3x–2y=12.Whichcouldbeanequationforanothersideoftherectangle?

(Calculators are ok from this point on…)

9. Whichsequenceisarithmetic?

A)48163264.... B)1112141721.... C)28152−11−24....D)30−2520−1510....

Graph given equation. REMEMBER: y = mx + b slope y-intercept

THINK An intercept is where the line crosses an x or y-axis. LOOK at the LABEL of the Y-AXIS AND the TITLE to determine the answer to this question.

10. Jayda makes a graph to show the weight of a jar when it contains different numbers of marbles.

What does the y-intercept represent? A)TheweightofeachmarbleB)TheweightofthejarbyitselfC)Thenumberofmarbleswhentheweightis0gramsD)Thenumberofmarbleswhentheweightis10grams Explain WHY you chose this answer: _______________________________ _______________________________________________________________

11. Anequationisshown.m=4p+3Whenpisincreasedby2,howmuchdoesmincrease?

A)2B)4C)7D)8

THINK 1. What does m = __ when p = 1?

2. “Increase” means +. How much do you add to 1? 1 + 2 = 3

3. What does m = ___ when p = 3?

4. How much did p increase (go up)?

THINK Associative: You CHANGE the GROUP you hang out with (+ or •).

Examples: (a + b) + c = a + (b + c) (a • b) • c = a • (b • c) Commutative: You MOVE to “commute” from school to home (+ or •).

Examples: a + b = b + a a • b = b • a Distributive: You SHARE (MULTIPLY) the OUTSIDE with the (INSIDE). “Rainbow” property

Examples: a(b + c) = ab + ac -OR- ab + ac = a(b + c) Identity: The number keeps its “identity” (SAME #).

Examples: a + 0 = a a • 1 = a

12.Asequenceisshown.Whatistheseventhterminthesequence? 1.5 4.5 13.5 40.5…

A)121.5B)364.5C)1,093.5D)3,280.5

13. Whichpropertyisusedintheequation:mg+mh=m(g+h)?

A)AssociativeB)CommutativeC)Distributive D)Identity

THINK Is this sequence Arithmetic or Geometric?

_______________ WHY? I have to MULTIPLY by 3 each

time to find the next term.

Two Solution Methods 1. EXTEND the PATTERN to the 7th term

(you have 1-4 already).

2. Formula: a • (r) n – 1 a = first # n = # you want to find r = ratio

THINK RULE: The expression INSIDE the absolute value symbol can be either positive or negative.

| ax + b | = c means ax + b = c OR ax + b = -c

Positive Negative 2x – 4 = 6 2x – 4 = -6

THINK

*Isolate the terms inside the | | and make the ANSWER BOTH + and -. To find the other solution just solve for x.

14. Whichequationisthesamelineas y=3x−8?

A)3x−2y=8B)−3x−2y=−8C)6x−y=16D)6x−2y=16

15.Anequationisshown.

|2x–4|=6

Theequationhas2solutions.

Onesolutionisx=5.

Whatistheothersolution?

THINK REWRITE each equation in slope-intercept form: y = mx + b Which one is the SAME? SHOW ALL WORK!!!

THINK

Two Solution Methods

“Distance” means distance formula:

€

x2 − x1( )2+ y2 − y1( )2

OR Plotting on a coordinate plane and using the Pythagorean Theorem (a2+ b2= c2)

16. Lisahas5moregreenmarblesthanbluemarbles.Shehasatotalof40greenandbluemarbles.Whichsystemofequationsrepresentsthissituationifxisthenumberofgreenmarblesandyisthenumberofbluemarbles?

A)

€

y= x +5x +y= 40

B)

€

x= y+5x +y= 40

C)

€

y= x +5y= x +40

D)

€

x= y+5x=y+40

17. Whatisthedistancebetween(4,7)and(­3,9)onacoordinategrid? A)

€

5

B)

€

45

C)

€

53

D)

€

305

THINK “More” means + “Total” means =

Word Equation:

Green = x Green and Blue = 40 Blue = y _ + _ = 40

THINK of the pattern…

Blue Green 1 6 2 7 3 __

What is the equation? Blue + _ = Green (Assign x and y) y + _ = x

THINK Arithmetic Sequences have a COMMON DIFFERENCE (Add or Subtract the SAME number) to extend the pattern….

Formula: f(x) = mx + b

The common difference IS the slope (m). Find what came BEFORE -1 (the ZERO term #) – this IS the y-intercept (b). *Because the y-intercept is the value of y when x = 0.

THINK Substitute for x and y then solve.

18. Whichfunctionformsageometricsequencewhenx=1,2,3,…?A)

€

f(x)=x+2

B)

€

f(x)=x2

C)

€

f(x)=x2 + 2

D)

€

f(x)=2x

19. Asequenceisshown.Whatisthefunctionruleforthesequence?

­1 ­7 ­13 ­19 ­25 …

A)

€

f(x)=x-6B)

€

f(x)=-6x

C)

€

f(x)=5x-6D)

€

f(x)=-6x-5

20. Whatisthevalueof­3|­2x–y|whenx=­4andy=5? SHOWYOURWORK!

A)‐27B)‐9C)9D)27

THINK Geometric Sequences have a COMMON RATIO (MULTIPLY by the SAME number) to extend the pattern. Formula: f(x) = a(b)x

THINK “each” means • or ÷

TIP Draw a picture

THINK This is a 2-Step equation. What comes first? ___

THINK Steps:

1. Isolate the variable (x) in each inequality.

2. Remember… < means numbers that are LESS than > means numbers that are MORE than

21. Leonplants3rowsoftomatoeswithnplantsineachrow.Healsoplants

1rowofbeanswith5plantsintherow.Whichequationcanbeusedtofindt,thetotalnumberofplantsLeonplanted?

A)

€

t =n+8B)

€

t =3n+1C)

€

t =3n+5 D)

€

t =5n+322. Whatisthevalueofpwhen2p+10=24? SHOWYOURWORK!

A)p = 7B)p = 12C)p = 17D)p = 28

23. Anumberlineisshown.

Whichinequalityhasthesolutionshownonthenumberline?

A)

€

-4>x>-2B)

€

4 <-2x <8 C)

€

4>-2x>8 D)

€

-4 <2x <-8

THINK We use the PYTHAGOREAN THEOREM to find the length of LEGS (AB and BC) or the HYPOTENUSE (AC) of RIGHT triangles. Formula: a2 + b2 = c2 Steps:

1. Formula 2. Substitute 3. Solve 4. Remember to find the !

THINK 1. Find the slope of the line. 2. What is the slope of a line perpendicular to that? ______ 3. Starting at the given point, draw in your NEW slope. What is your y-intercept? __________ Slope-intercept form: y = mx + b slope y-intercept

24. Atriangleisshown. WhatisAC? 25. Thegraphofalineisshown.

Whatistheequationofalinethatisperpendiculartothelineshownandgoesthroughthepoint(3,­1)?

A)

€

y=-43

x−5

B)

€

y=-43

x +3

C)

€

y= 43

x−5

D)

€

y= 43

x +3

THINK Base your decision solely on the given data and the trend of the data line.

26. ThescatterplotshowstheheightsofFerriswheelsandtheyearstheywerebuilt.

Whichstatementistrueaboutthescatterplot?

A)AllFerriswheelsbuildbefore1980musthavebeenlessthan60meters

high.B)Basedonthelineofbestfit,Ferriswheelheightsincreaseabout25

metersevery10years.C)EachFerriswheelistallerthanallFerriswheelsthatwerebuiltearlier.D)Eachyear,moreFerriswheelswerebuiltthantheyearbefore.